GREENBURGH, N.Y. — The anchor of the Dallas Mavericks’ defense now centers one of the league’s best frontcourts.

Tyson Chandler joined the New York Knicks on Saturday, in the belief that joining, Carmelo Anthony and Amare Stoudemire means he’s not done competing for championships.

The Knicks have long needed a defensive presence, and Chandler plans to provide it.

“I know what my job is coming here,” he said. “I know I came here to defend. I’m going to defend the rim, I’m going to rebound, I’m going to get extra shots. And I think if we play on both ends and play as a team, the sky is definitely the limit for this squad.”

Chandler gets a four-year contract worth about $56 million after coming to the Knicks via sign-and-trade as part of a three-team deal. The Knicks sent Ronny Turiaf and cash to the Washington Wizards and reserve guard Andy Rautins to the Mavericks, and there were other picks involved.

The Knicks also waived point guard Chauncey Billups and designated him as their amnesty player so they could afford Chandler.

The 7-foot-1 Chandler helped the Mavericks win the NBA championship last season, averaging 10.1 points and 9.4 rebounds, and at first hoped he would return to Dallas. But the Mavericks wanted to keep other options open, and when the Knicks emerged as a surprising option, they quickly become Chandler’s preferred one.

“The Knicks were never on my radar. I’d never seen them as being a possibility and once I got word that it could potentially happen, they became my No. 1 priority was to get here,” Chandler said.

It took some work, notably using the amnesty clause to waive Billups so his $14.2 million salary wouldn’t count for salary cap or luxury tax purposes. Billups was their starting point guard last season after coming with Anthony in a trade from Denver and was expected to return, with the Knicks picking up his option for this season in April when they would have owed him just $3.7 million had they waived him within five days after the season ended.

“We didn’t want to get rid of Chauncey and when I talked to him today I told him, ‘Chauncey, it’s not like we’re waiving you because we don’t want you. Look at it as what it is. We traded you basically for the starting center on the NBA championship team,’” interim general manager Glen Grunwald said.

Long undersized — Dwight Howard blocked more shots than they did as a team two seasons ago — the Knicks eagerly welcomed the 225-pound Chandler. His No. 6 jersey — guard Landry Fields switched to No. 2 so Chandler could have it — covered most of Madison Square Garden chairman James Dolan’s body when he held it up for a photo.

Chandler later posed alongside Anthony and Stoudemire, two of league’s elite scorers. Now the Knicks have a stopper, too.

“Last year was an amazing run and I think after you win a championship it’s hard to go backwards,” Chandler said, “and the only thing I wanted in free agency was an opportunity to continue to chase that dream and continue to win championships.”

Though it was often believed the Knicks wouldn’t be spenders this offseason while saving their money for free agency in 2012, Grunwald felt adding a player such as Chandler was a better strategy for building a contender.

“When we looked at things this past summer and over the fall, we said it’d be great to get someone like Tyson Chandler. Well, we got Tyson Chandler, so that’s even better,” he said.

“Our plans haven’t changed. Tyson was the top of our list in terms of free agents this year. We took a look at everything, we felt this was the best move for us to build a team both in the short term and in the long term.”